We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
@article{bwmeta1.element.doi-10_1515_agms-2015-0012,
author = {L. Cavallina and A. Colesanti},
title = {Monotone Valuations on the Space of Convex Functions},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1321.26027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0012}
}
L. Cavallina; A. Colesanti. Monotone Valuations on the Space of Convex Functions. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0012/
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